Output feedback vibration control of a string driven by a nonlinear actuator

Abstract

• A wave partial differential equation sandwiched by nonlinear and linear ordinary differential equations is considered. • An observer is designed to estimate full states of the overall system only using available boundary values. • An observer-based output feedback boundary controller is proposed via the backstepping method. • The global exponential stability of the output feedback closed-loop system is proved by Lyapunov analysis. In this paper, we design an observer-based output feedback controller to exponentially stabilize a system of nonlinear ordinary differential equation-wave partial differential equation-ordinary differential equation. An observer is designed to estimate the full states of the system using available boundary values of the partial differential equation . The output feedback controller is built via the combination of the ordinary differential equation backstepping which is applied to deal with the nonlinear ordinary differential equation, and the partial differential equation backstepping which is used for the wave partial differential equation-ordinary differential equation. The controller can be applied into vibration suppression of a string-payload system driven by an actuator with nonlinear characteristics. The global exponential stability of all states in the closed-loop system is proved by Lyapunov analysis. The numerical simulation illustrates the states of the actuator, string, payload and the observer errors are fast convergent to zero under the proposed output feedback controller.